Since you are renting I doubt you could replace them without the landlord's permission, but what are indeed called "mixer taps" are available from any builders-merchants or stockists of plumbing materials.

They are not attachments on the existing taps though, as I think you are asking for but are very unlikely to find.

Instead a mixer-tap is a complete fitting combining both taps in one unit, fed from both the hot and cold water pipes. They are very common on kitchen sinks, perhaps less so on washbasins.

Anyway separate taps are no more or less "useless" in Winter than mixer-taps, provided they and the pipework are protected from freezing. If that is the problem, you need have the pipes lagged properly.

Yeah if your renting though i doubt you can add to the plumbing.

Im not needed.

Put the plug in and fill with equal amounts or to your desired temperature and then wash your hands

Need a new faucet.

Live the rough life -- put the plug in the basin and mix the water there.

The only, (easy push on type), i could find were these:
Im pretty sure you can cut them amd make them shorter

You just turn on both hot and cold taps to get warm water